Should speakers be upgraded before preamp and amplifiers?

I would assemble a completely new system. Yes, first choose the speakers. $15k is not little, especially if you buy used pieces, at least some of them.

@daveoman 

If you’re simply asking which next component to change, then it’s the amp.

BUT, it sounds like you want to change both speakers and amps soon, so I suggest demoing speakers maybe 3-10k range, then get matching electronics.  

Oh dear. You have it backwards. Improve your turntable to a Technics SL1300G/Nagaoka MP500 and replace the old receiver with something like a VAC integrated for $7k all in, and you won’t need to replace the Von Schweikerts.

Yeah, this might work out fine if the speakers are good enough for that.

@daveoman  Could I suggest you start with your room.  The dimensions you have stated do not produce good results from a couple of acoustic calculators I use.  They say the room is half the equation to a great system.  Just a thought.  Cheers.